![](/images/graphics-bg.png)
Global Existence of Solutions for a Nonstrictly Hyperbolic System
Joint Authors
Zheng, De-yin
Lu, Yun-guang
Song, Guo-qiang
Lu, Xue-zhou
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-31
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We obtain the global existence of weak solutions for the Cauchy problem of the nonhomogeneous, resonant system.
First, by using the technique given in Tsuge (2006), we obtain the uniformly bounded L ∞ estimates z ( ρ δ , ε , u δ , ε ) ≤ B ( x ) and w ( ρ δ , ε , u δ , ε ) ≤ β when a ( x ) is increasing (similarly, w ( ρ δ , ε , u δ , ε ) ≤ B ( x ) and z ( ρ δ , ε , u δ , ε ) ≤ β when a ( x ) is decreasing) for the ε -viscosity and δ -flux approximation solutions of nonhomogeneous, resonant system without the restriction z 0 ( x ) ≤ 0 or w 0 ( x ) ≤ 0 as given in Klingenberg and Lu (1997), where z and w are Riemann invariants of nonhomogeneous, resonant system; B ( x ) > 0 is a uniformly bounded function of x depending only on the function a ( x ) given in nonhomogeneous, resonant system, and β is the bound of B ( x ) .
Second, we use the compensated compactness theory, Murat (1978) and Tartar (1979), to prove the convergence of the approximation solutions.
American Psychological Association (APA)
Zheng, De-yin& Lu, Yun-guang& Song, Guo-qiang& Lu, Xue-zhou. 2014. Global Existence of Solutions for a Nonstrictly Hyperbolic System. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1014590
Modern Language Association (MLA)
Zheng, De-yin…[et al.]. Global Existence of Solutions for a Nonstrictly Hyperbolic System. Abstract and Applied Analysis No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-1014590
American Medical Association (AMA)
Zheng, De-yin& Lu, Yun-guang& Song, Guo-qiang& Lu, Xue-zhou. Global Existence of Solutions for a Nonstrictly Hyperbolic System. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1014590
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014590